Huntsville Quality Tree Service does both, and they are genuinely different jobs rather than two names for the same thing.
Grinding uses a machine to chip the stump down below grade, leaving the root system in the ground. It runs $100 to $400 per stump here.
Full removal extracts the stump and the root plate, which means excavation, a much larger hole, and considerably more disruption to the surrounding yard.
For most homeowners grinding is the right answer. The exception is when something is going where the stump was. Below is how to tell which case you are in.

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A grinder chips the stump into mulch, typically to somewhere between four and twelve inches below grade depending on what you need.
What is left is a hole full of wood chips and the entire root system still in the soil, out of sight. Backfill it with the chips or with soil, and grass grows over it.
Pricing depends on stump diameter, wood species, root spread and access. A single stump in an open front yard costs less than a large oak stump wedged between a fence and a foundation — see our stump grinding page.
Removal takes out the stump and the major roots, which requires machinery and digging. It leaves a substantial hole needing fill, and it disturbs a much wider area of the yard.
It costs more, takes longer and makes a bigger mess. It is also the only option when what happens next needs clear ground.
Which is most situations. The roots left behind decay in place over several years and cause no problem while they do.
That last one is the case we are most often called about. Roots that have found a sewer line or lifted a walkway do not stop doing so because the tree above them is gone.
Replanting is the one people get wrong. Putting a new tree directly into ground full of old roots and decaying wood works poorly — the soil chemistry is wrong and the space is occupied. Either remove properly or plant somewhere else.
They decay over several years. As they do, the soil above them settles, so a ground stump area often needs topping up with soil once or twice in the first couple of years. That is normal rather than a fault.
Decaying roots can also produce fungi in the lawn for a season or two. Harmless, and it passes.
Grinding produces a surprising volume of mulch — considerably more than the stump appears to hold, because the material expands as it is chipped.
You can leave it in the hole as backfill, spread it as mulch elsewhere, or have it hauled away. Worth deciding in advance, since it affects both the tidiness of the finish and the price. Fresh chips are not ideal as planting mulch straight away, since they draw nitrogen as they break down.
If you are having a tree taken down, deal with the stump at the same time. The crew and equipment are already on site, and combining the work is cheaper than bringing someone back for it.
Our tree removal page covers what a removal quote should include, and stump work is one of the items worth settling in writing rather than assuming.
Tell us what is going in that spot afterwards and we will tell you which one you need. Call 256-203-9294.
Huntsville Quality Tree Service works throughout Huntsville and Madison County, including Madison, Athens, Decatur, Monrovia, Harvest, Meridianville, Hazel Green, Big Cove, Owens Cross Roads, New Market & more.